9. Prove that I-n

--2 <0.01.

I-n n2 + 2n + 3 < 0.025.

2n3 + 5n2 + 8n + 3 n-l 3 2 1 < 0.002. n -n +n-

(a1b1 + a2b2)2 ::; (a~ + a~)(b~ + b~)

for all a1,a2,b1,b2 E R.